Bianchi, 23, was Force India reserve last season.
The Frenchman will test for the team at Barcelona on Saturday and then complete half a day of running on Sunday, and pending final signature on his deal will make his debut in the Australian Grand Prix later this month.
Marussia team boss John Booth said the squad had to drop Razia having previously released Timo Glock in order to secure its financial future.
AUTOSPORT revealed earlier on Friday that Bianchi would replace Razia for the 2013 Formula 1 season as the Brazilian's backers had missed the deadline for a second payment.
The team had parted with the salaried Glock in January because it needed drivers who could bring funding this season.
"We have found ourselves in a situation where we have had to terminate our contract with Luiz Razia," said Booth.
"Having made clear the basis on which we must operate in 2013, and given the steps we had taken to put that new structure in place, we had no alternative but to remain true to the principles which we had identified as being key to securing our long-term future."
Booth added that he was delighted to be able to secure a replacement of Ferrari protege and 2012 Formula Renault 3.5 runner-up Bianchi.
"Jules is a proven talent who is highly regarded within the paddock," said Booth.
"He has been on a clear trajectory towards Formula 1 and has achieved some impressive performances through the various feeder formulas, notably his 2012 season in Formula Renault 3.5 when he was also reserve driver for Force India.
"He is part of the Ferrari Driver Academy and his obvious pedigree put him on the radar for a number of teams over the winter as a driver ready to step up to Formula 1."
Bianchi was in a head to head with Adrian Sutil for the second Force India driver until the team opted for the German this week.